A mechanical system for processing workpieces, especially metal sheets, having a storage side, which comprises (a) a workpiece store, (b) a processing side, which has a plurality of mechanical processing units, and (c) a mechanical feeding device between the storage side and the processing side is disclosed in US 2003/0091423 A1. In this system the feeding device allows workpieces to be picked up at the storage side and delivered at the processing side and/or picked up at the processing side and delivered at the storage side. A storage rack is provided in which the metal sheets that are to be processed are stored. Processing of the workpieces is performed by means of processing machines, especially by means of laser cutting machines, which are arranged in succession in the direction of movement of the feeding device. All the processing machines of this system are served by the feeding device. By means of the feeding device, metal sheets to be processed are taken out of the storage rack, then transported to the relevant processing machine and finally transferred back to the storage rack.